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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 76531b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
76531.b2 | 76531b1 | \([0, -1, 1, -6167, 188812]\) | \(-43614208/91\) | \(-54128922211\) | \([]\) | \(91728\) | \(0.94514\) | \(\Gamma_0(N)\)-optimal |
76531.b3 | 76531b2 | \([0, -1, 1, 10653, 923005]\) | \(224755712/753571\) | \(-448241604829291\) | \([]\) | \(275184\) | \(1.4944\) | |
76531.b1 | 76531b3 | \([0, -1, 1, -98677, -29372338]\) | \(-178643795968/524596891\) | \(-312042464890895011\) | \([]\) | \(825552\) | \(2.0438\) |
Rank
sage: E.rank()
The elliptic curves in class 76531b have rank \(1\).
Complex multiplication
The elliptic curves in class 76531b do not have complex multiplication.Modular form 76531.2.a.b
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.